What they're describing isn't time travel debugging - https://en.wikipedia.org/wiki/Time_travel_debugging.

I'd call this logging calls to your business logic layer. Then running the logged calls on your business logic layer in a development environment to debug the problem.

Your business logic layer should be separate from your UI/presentation layer.

Makes it easy to test them separately if they're not tightly coupled.

Also if you wanna to reuse your business logic layer in a different UI environment, it's easier to switch to another UI if they're not tightly coupled.